Explain LC Resonance in a Circuit

[Dracovich]

Hey guys, I'm doing a lab report on an LC resonant circuit, and it's I've kinda hit a speedbump in trying to explain why exactly the resonance is happening.

I don't know if "LC resonant circuit" is a normal thing to call it so i'll explain a bit. You have V_in which goes into a resistor, then the line splits up into V_out on one side, and a capacitor and inductor connected in parallel on the other side.

So this circuit let's through pretty specific frequencies, and i can talk about it mathmatically that when $$\omega$$ is at different values i can see different things. But i was wondering if i could explain it a bit more detailed, trying to explain why physically it happens at those places.

My first thought was trying to think of it in terms of a normal resonance frequency of a standing wave (thinking of a string with two fixed points being vibrated), so if V_out has a much higher impedence then the LC part, then it could be thought of as a fixed point (total reflected wave), but the LC circuit was not, so it just passed through there easily with not much going to V_out, but at certain frequencies (depending on the values of L and C) the impedence of the LC circuit grew so high that it became a fixed point as well and reflected waves completely (although at that point it all goes through V_out i guess since it has a finite impedence, and that would no longer be a fixed point).

But i don't know, my reasoning doesn't seem very solid and i would like to hear from you guys if you had any good thoughts on the matter.

 

[berkeman]

A good way to think about it is in terms of the Z impedance presented to the circuit by the parallel LC. Think about what happens in the LC for a moment -- the energy stored flows back and forth between the voltage across the cap (energy stored in the electric field across the cap) and the current through the inductor (energy stored in the magnetic field of the inductor). The current is max when the voltage across the cap is zero, and the voltage across the cap is max when the current through the inductor is zero. You get a resonance back and forth in the energy storage, and in the transfer of that energy via the voltage and current.

Now, once you get this resonance going, and if there is not much loss in the circuit, then you can disconnect the driving voltage source and let the oscillations continue on their own. So in this state, it takes very little energy input to keep the resonance going, or in other words, the parallel LC circuit has a high input impedance in this state (being driven near resonance). The lower the resistive losses in the parallel LC, the higher the "Q", and the higher the apparent input impedance at resonance.

So, when you have a circuit with an AC voltage source feeding a parallel LC through a resistor, you basically get a voltage divider, and at resonance, you get all of the input voltage carried through to the output, because the LC is in resonance and presents a high impedance to the divider with the input resistance.

Does that make sense? Quiz question -- what if it is a series LC instead of parallel LC? What is different, and what does the output voltage do at resonance?

 

[piercas]

LC resonance in a circuit occurs when the inductance (L) and capacitance (C) in the circuit are balanced in such a way that the circuit's natural frequency (also known as the resonant frequency) is achieved. This means that the reactive components (inductance and capacitance) cancel each other out, resulting in a purely resistive circuit.

At this resonant frequency, the voltage across the capacitor and the current through the inductor are in phase with each other, creating a standing wave effect. This means that the energy stored in the inductor is transferred to the capacitor and back again, resulting in a continuous oscillation at the resonant frequency.

To better understand this concept, think of the LC circuit as a swing set. The inductor is the seat of the swing, while the capacitor is the chains. When the swing is at its lowest point, it has the most potential energy (stored in the inductor). As the swing moves up, the potential energy is converted into kinetic energy (current flowing through the circuit). When the swing reaches its highest point, all of the potential energy has been converted into kinetic energy and the swing comes to a stop. At this point, the kinetic energy is converted back into potential energy (stored in the capacitor) and the swing starts moving in the opposite direction. This back and forth motion continues, creating a resonant frequency.

In terms of the circuit, this means that at the resonant frequency, the voltage across the capacitor and the current through the inductor are at their maximum amplitudes. This also means that the impedance of the circuit is at its minimum, allowing the signal to pass through easily. At other frequencies, the impedance of the circuit may be higher, resulting in a weaker signal or no signal at all.

In summary, LC resonance in a circuit occurs when the reactive components are balanced and the circuit's natural frequency is achieved. This results in a standing wave effect and a transfer of energy between the inductor and capacitor, allowing the signal to pass through easily at the resonant frequency.